Question

# The mean weight of $$9$$ items is $$15$$. If one more item is added to the series the mean becomes $$16$$. The value of the $$10^{th}$$ item is

A
35
B
30
C
25
D
20

Solution

## The correct option is C $$25$$Assuming original nine elements are $$x_1, x_2, x_3, .........x_9$$ and new element is $$x$$Sum of original nine elements is $$\displaystyle\sum_{i=1}^9x_i =9\times 15=135$$Given new mean after addition of $$x$$ is 16. $$\Rightarrow \cfrac{\displaystyle \sum_{i=1}^9x_i + x}{10} = 16$$$$\Rightarrow \cfrac{135+x}{10}=16 \Rightarrow x= 160-135 = 25$$Mathematics

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